TY - JOUR

T1 - W-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions

AU - Dinar, Yassir Ibrahim

N1 - Funding Information:
The author thanks B. Dubrovin for useful discussions and N. Pagnon for providing Ref. [21] . Part of this work was inspired by the “Summer School and Conference in Geometric Representation Theory and Extended Affine Lie Algebras” at the University of Ottawa, organized by the Fields Institute. This work is partially supported by the European Science Foundation Programme (grant no. MISGAM-2116 ) “Methods of Integrable Systems, Geometry, Applied Mathematics” (MISGAM). The author also likes to thank anonymous reviewers who gave corrections and valuable comments that has helped to improve the quality of the manuscript.

PY - 2014/10

Y1 - 2014/10

N2 - We prove that the classical W-algebra associated to a nilpotent orbit in a simple Lie-algebra can be constructed by preforming bihamiltonian, Drinfeld-Sokolov or Dirac reductions. We conclude that the classical W-algebra depends only on the nilpotent orbit but not on the choice of a good grading or an isotropic subspace. In addition, using this result we prove again that the transverse Poisson structure to a nilpotent orbit is polynomial and we better clarify the relation between classical and finite W-algebras.

AB - We prove that the classical W-algebra associated to a nilpotent orbit in a simple Lie-algebra can be constructed by preforming bihamiltonian, Drinfeld-Sokolov or Dirac reductions. We conclude that the classical W-algebra depends only on the nilpotent orbit but not on the choice of a good grading or an isotropic subspace. In addition, using this result we prove again that the transverse Poisson structure to a nilpotent orbit is polynomial and we better clarify the relation between classical and finite W-algebras.

KW - Bihamiltonian reduction

KW - Dirac reduction

KW - Drinfeld-Sokolov reduction

KW - Slodowy slice

KW - Transverse poisson structure

KW - W-algebras

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U2 - 10.1016/j.geomphys.2014.06.003

DO - 10.1016/j.geomphys.2014.06.003

M3 - Article

AN - SCOPUS:84903614163

SN - 0393-0440

VL - 84

SP - 30

EP - 42

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -